Find the greatest and the smallest real numbers.
(i) 2√3, 3/√2, -√7, √15
(ii) -3√2, 9/√5, -4, 4/3 √5, 3/2√3
Solution:
(i) 2√3, 3/√2, -√7, √15
Let us simplify each fraction
2√3 = √(4×3) = √12
3/√2 = (3×√2)/(√2×√2) = 3√2/2 = √((9/4)×2) = √(9/2) = √4.5
-√7 = -√7
√15 = √15
So,
The greatest real number = √15
Smallest real number = -√7
(ii) -3√2, 9/√5, -4, 4/3 √5, 3/2√3
Let us simplify each fraction
-3√2 = -√(9×2) = -√18
9/√5 = (9×√5)/(√5×√5) = 9√5/5 = √((81/25)×5) = √(81/5) = √16.2
-4 = -√16
4/3 √5 = √((16/9)×5) = √(80/9) = √8.88 = √8.8
3/2√3 = √((9/4)×3) = √(27/4) = √6.25
So,
The greatest real number = 9√5
Smallest real number = -3√2
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